Pre-requisites Module 13: Multiple Membership Multilevel Models Modules 1-5,11,12 MLwiN Practical 1 George Leckie and Dewi Owen Centre for Multilevel Modelling Contents Introduction to the Patient Satisfaction Dataset... 3 P13.1 Examining and Describing the Data... 6 P13.1.1 Exploring the multiple membership data structure... 7 P13.1.2 Summarising the response and predictor variables... 13 P13.2 A Multiple Membership Model of Satisfaction... 15 P13.2.1 Specifying and fitting the multiple membership model... 15 P13.2.2 Interpretation of the model output... 26 P13.2.3 Calculating coverage intervals, variance partition coefficients (VPCs) and intraclass correlation coefficients (ICCs)... 27 P13.2.4 Predicting and examining nurse effects... 31 P13.3 Exploring Alternative Multiple Membership Weighting Schemes... 36 P13.4 Adding Predictor Variables... 40 P13.4.1 Adding patient level predictor variables... 40 P13.4.2 Adding nurse level predictor variables... 42 P13.5 Adding Random Coefficients... 46 P13.5.1 Adding cross-level interactions... 46 Further Reading... 47 References... 48 1 This MLwiN practical is adapted from the corresponding Stata practical: Leckie, G. (2013). Multiple Membership Multilevel Models MLwiN Practical. LEMMA VLE Module 12, 1-45. Accessed at http://www.bristol.ac.uk/cmm/learning/course.html. Centre for Multilevel Modelling, 2013 1
If you find this module helpful and wish to cite it in your research, please use the following citation: Leckie, G. and Owen, D. (2013). Multiple Membership Multilevel Models MLwiN Practical. LEMMA VLE Module 13, 1-48. http://www.bristol.ac.uk/cmm/learning/course.html Address for correspondence: George Leckie Centre for Multilevel Modelling University of Bristol 2 Priory Road Bristol, BS8 1TX UK g.leckie@bristol.ac.uk Centre for Multilevel Modelling, 2013 2
Introduction to the Patient Satisfaction Dataset We will analyse simulated data based on a fictitious patient survey carried out in a local hospital. In this fictitious survey, hip replacement patients were asked to score how satisfied they were with the level of care provided to them by hospital nurses during their recent hospital stay. We expect nurses to play an important role in the scores patients give with patients reporting more favourably when cared for by certain nurses. Ultimately, the hospital wants to learn what it is about these nurses which results in patients reporting better hospital experiences. Armed with such knowledge, the hospital would then like to implement additional training for all nurses with the ultimate goal of improving all patients hospital experiences. During the course of their hospital stays, most patients were cared for by multiple nurses and so the data are more complex than a simple two-level hierarchy of patients nested within nurses. Rather the data are characterised by a nonhierarchical multiple membership structure whereby patients (level 1) are multiple members of nurses (level 2). The simulated data consist of 1,000 patients who, between them, were cared for by 25 nurses. Four hundred patients were cared for by only one nurse during their stay, 300 patients were cared for by two nurses, 200 patients by three nurses, and 100 patients by four nurses. The data record which nurses cared for which patients. The response variable is a continuous measure of patients overall satisfaction with the care they received during their hospital stay. The data also record a continuous measure of patients likelihood of having a successful operation calculated at a preoperative assessment clinic. The score is based on patients current medical fitness, their medical history and any other factors that might lead to complications with their operation. Both scores are standardised to have zero means and variances of one. The multilevel modelling routines in different software packages require data describing the multiple membership structure (i.e. the nurse identifiers and the proportion of time each patient is cared for by each nurse) to be stored in one of two different forms: compact form or wide form. 2 Both forms have one row per patient, but store the multiple membership information using different sets of variables. In this dataset, we store these data twice, once in each form so that we can contrast the two approaches. Compact form consists of two sets of variables: the multiple membership ID variables n1st to n4th which record the first, second, third and fourth nurse that cared for each patient and the associated multiple membership weight variables p1st to p4th which record the proportion of time cared for by each of these 2 For example, the multilevel modelling classical estimation routines in MLwiN require these data to be in wide form, while the Bayesian routines in MLwiN only accept these data in compact form. The multilevel modelling routines in Stata and R only accept the multiple membership information in wide form. Centre for Multilevel Modelling, 2013 3
nurses. 3 Wide form carries the same information in one set of variables, p1 to p25, which records the proportion of time each patient is cared for by each of the 25 nurses. 4 For example, p1 reports the proportion of time cared for by nurse 1, p2 the proportion of time cared for by nurse 2, and so on, up until p25, the proportion of time cared for by nurse 25, the final nurse. The data contain a single nurse level variable, a measure of how happy nurses feel about their jobs. This nurse level variable is also stored in the dataset in both compact (h1st, h2nd, h3rd and h4th) and wide (h1 to h25) forms. 3 Had the maximum number of nurses seen by any patient been five rather than four, then there would have been five multiple membership ID variables and five associated multiple membership weight variables rather than four. 4 In this example wide form is a less efficient means of storage than compact form as it takes 25 variables to store the multiple membership information compared to eight variables for compact form. Centre for Multilevel Modelling, 2013 4
The dataset contains the following variables Variable name patient Description and codes Patient ID satis Patient postoperative satisfaction score. Scores are (approximately) standardised to have a mean of zero and a variance of one, with a higher score indicating a more satisfied patient. cons assess nurses n1st n2nd n3rd n4th p1st p2nd p3rd p4th h1st h2nd h3rd h4th A column of ones. This variable will be included as an explanatory variable in all models and its coefficient will be the intercept. Patient preoperative assessment score. Scores are standardised to have a mean of zero and a variance of one, with a higher score indicating a patient that was assessed to be more likely to have a successful operation. Number of nurses seen by patient Nurse ID for patient's 1st nurse Nurse ID for patient's 2nd nurse Nurse ID for patient's 3rd nurse Nurse ID for patient's 4th nurse Prop. time cared for by 1st nurse Prop. time cared for by 2nd nurse Prop. time cared for by 3rd nurse Prop. time cared for by 4th nurse Happiness score for 1st nurse Happiness score for 2nd nurse Happiness score for 3rd nurse Happiness score for 4th nurse p1 Prop. time cared for by nurse 1 p2 Prop. time cared for by nurse 2 p25 Prop. time cared for by nurse 25 h1 Happiness score for nurse 1 h2 Happiness score for nurse 2 h25 Happiness score for nurse 25 Centre for Multilevel Modelling, 2013 5
P13.1 Examining and Describing the Data Load 13.1.wsz into memory and open the do-file for this lesson From within the LEMMA learning environment Go to Module 13: Multiple Membership Multilevel Models, and scroll down to MLwiN datafiles Click 13.1.wsz to open the worksheet The Names window will appear. The data consist of 1,000 observations on 67 variables and each variable has been given a variable label (description). We see, for example, that the response variable satis ranges from -2.982 to 3.041. We shall describe a range of summary statistics for the response and predictor variables in P13.1.2. Centre for Multilevel Modelling, 2013 6
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